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ON PLANAR FUZZY TERNARY RINGS

Year 2011, Volume: 60 Issue: 1, 1 - 8, 01.02.2011

Ziya Akça Rüstem Kaya

https://doi.org/10.1501/Commua1_0000000664

Abstract

In this paper, we extend the process of coordinatization of projective planes to the fuzzy pro jective planes and introduce notion of fuzzy
ternary ring which determines its associated fuzzy pro jective plane. Later, we
give some propositions concerned with linearity of the defined fuzzy ternary
operation.

Keywords

Fuzzy projective plane Fuzzy ternary ring Planar fuzzy ternary ring

References

  • [1] Z. Akça, I. Günaltılı, Ö. Güney, On the Fano Subplanes of the Left Semifield Plane of order ˙ 9, Hacettepe Journal of Mathematics and Statistics, Volume 35 (1) (2006) 55-61.
  • [2] Z. Akça, A. Bayar, S. Ekmekçi, On the Classification of Fuzzy pro jective lines of Fuzzy 3- dimensional pro jective spaces, Communications Mathematics and Statistics, Vol. 55(2) (2007) 17-23.
  • [3] S. Ekmekçi, A. Bayar, Z. Akça, On the Classification of Fuzzy pro jective planes of Fuzzy 3-dimensional pro jective spaces, Chaos, Solitons and Fractals 40 (2009) 2146-2151.
  • [4] A. Bayar, Z. Akça, S. Ekmekçi, A Note on Fibered Pro jective Plane Geometry, Information Science 178 (2008) 1257-1262.
  • [5] S. Çiftçi, R. Kaya, On the Fano Subplanes in the Translation Plane of order 9, Doga-Tr. J. ˘ of Mathematics 14, (1990) 1-7.
  • [6] K.C. Gupta, S. Ray, Fuzzy Plane Pro jective Geometry, Fuzzy Sets and Systems 54 (1993) 191-206.
  • [7] R. Kaya, Pro jektif Geometri, Osmangazi University (2005).
  • [8] R. Kaya, On the Connection Between Ternary Rings and the Restricted Dual Pappus Theorems-I, J. of the FAC. of SC. of the K.T.Ü. vol. III. No. 6 (1981) 49-57.
  • [9] R. Kaya, On the Connection Between Ternary Rings and the Restricted Dual Pappus Theorems-II, Metu J. of pure and applied sciences, vol. 17. No. 1(1984) 63-68.
  • [10] L. Kuijken, H. Van Maldeghem, On the definition and some conjectures of fuzzy pro jective planes by Gupta and Ray, and a new defnition of fuzzy building geometries, Fuzzy Sets and Systems 138 (2003) 667-685.
  • [11] G. Pickert, Pro jective Ebenen ,Springer -Verlag, Berlin-Göttingen-Heidelberg, (1955).
  • [12] J. Yaqub, The Lenz-Barlotti classification, Proceeding of the pro jective geometry conference, University of Illinois, Chicago (1967) 129-162.
  • [13] L. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965) 338-358. Current address : Ziya Akça, Rüstem Kaya; Eski¸sehir Osmangazi University, Department of Mathematics and Computer Science, 26480, Eski¸sehir, Turkey E-mail address : zakca@ogu.edu.tr, rkaya@ogu.edu.tr URL: http://communications.science.ankara.edu.tr

Year 2011, Volume: 60 Issue: 1, 1 - 8, 01.02.2011

Ziya Akça Rüstem Kaya

https://doi.org/10.1501/Commua1_0000000664

Abstract

References

  • [1] Z. Akça, I. Günaltılı, Ö. Güney, On the Fano Subplanes of the Left Semifield Plane of order ˙ 9, Hacettepe Journal of Mathematics and Statistics, Volume 35 (1) (2006) 55-61.
  • [2] Z. Akça, A. Bayar, S. Ekmekçi, On the Classification of Fuzzy pro jective lines of Fuzzy 3- dimensional pro jective spaces, Communications Mathematics and Statistics, Vol. 55(2) (2007) 17-23.
  • [3] S. Ekmekçi, A. Bayar, Z. Akça, On the Classification of Fuzzy pro jective planes of Fuzzy 3-dimensional pro jective spaces, Chaos, Solitons and Fractals 40 (2009) 2146-2151.
  • [4] A. Bayar, Z. Akça, S. Ekmekçi, A Note on Fibered Pro jective Plane Geometry, Information Science 178 (2008) 1257-1262.
  • [5] S. Çiftçi, R. Kaya, On the Fano Subplanes in the Translation Plane of order 9, Doga-Tr. J. ˘ of Mathematics 14, (1990) 1-7.
  • [6] K.C. Gupta, S. Ray, Fuzzy Plane Pro jective Geometry, Fuzzy Sets and Systems 54 (1993) 191-206.
  • [7] R. Kaya, Pro jektif Geometri, Osmangazi University (2005).
  • [8] R. Kaya, On the Connection Between Ternary Rings and the Restricted Dual Pappus Theorems-I, J. of the FAC. of SC. of the K.T.Ü. vol. III. No. 6 (1981) 49-57.
  • [9] R. Kaya, On the Connection Between Ternary Rings and the Restricted Dual Pappus Theorems-II, Metu J. of pure and applied sciences, vol. 17. No. 1(1984) 63-68.
  • [10] L. Kuijken, H. Van Maldeghem, On the definition and some conjectures of fuzzy pro jective planes by Gupta and Ray, and a new defnition of fuzzy building geometries, Fuzzy Sets and Systems 138 (2003) 667-685.
  • [11] G. Pickert, Pro jective Ebenen ,Springer -Verlag, Berlin-Göttingen-Heidelberg, (1955).
  • [12] J. Yaqub, The Lenz-Barlotti classification, Proceeding of the pro jective geometry conference, University of Illinois, Chicago (1967) 129-162.
  • [13] L. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965) 338-358. Current address : Ziya Akça, Rüstem Kaya; Eski¸sehir Osmangazi University, Department of Mathematics and Computer Science, 26480, Eski¸sehir, Turkey E-mail address : zakca@ogu.edu.tr, rkaya@ogu.edu.tr URL: http://communications.science.ankara.edu.tr
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Ziya Akça This is me

Rüstem Kaya This is me

Publication Date February 1, 2011
Published in Issue Year 2011 Volume: 60 Issue: 1

Cite

APA Akça, Z., & Kaya, R. (2011). ON PLANAR FUZZY TERNARY RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 60(1), 1-8. https://doi.org/10.1501/Commua1_0000000664
AMA Akça Z, Kaya R. ON PLANAR FUZZY TERNARY RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2011;60(1):1-8. doi:10.1501/Commua1_0000000664
Chicago Akça, Ziya, and Rüstem Kaya. “ON PLANAR FUZZY TERNARY RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60, no. 1 (February 2011): 1-8. https://doi.org/10.1501/Commua1_0000000664.
EndNote Akça Z, Kaya R (February 1, 2011) ON PLANAR FUZZY TERNARY RINGS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60 1 1–8.
IEEE Z. Akça and R. Kaya, “ON PLANAR FUZZY TERNARY RINGS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 60, no. 1, pp. 1–8, 2011, doi: 10.1501/Commua1_0000000664.
ISNAD Akça, Ziya - Kaya, Rüstem. “ON PLANAR FUZZY TERNARY RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 60/1 (February 2011), 1-8. https://doi.org/10.1501/Commua1_0000000664.
JAMA Akça Z, Kaya R. ON PLANAR FUZZY TERNARY RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2011;60:1–8.
MLA Akça, Ziya and Rüstem Kaya. “ON PLANAR FUZZY TERNARY RINGS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 60, no. 1, 2011, pp. 1-8, doi:10.1501/Commua1_0000000664.
Vancouver Akça Z, Kaya R. ON PLANAR FUZZY TERNARY RINGS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2011;60(1):1-8.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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